One of the crown jewels of complexity theory is Valiant’s 1979 theorem that computing the permanent of an n*n matrix is #P-hard. Here we show that, by using the model of linear-optical quantum computing—and in particular, a universality theorem due to Knill, Laflamme, and Milburn—one can give a different and arguably more intuitive proof of this theorem.

For decades, Harvard’s Leslie Valiant has obviously deserved a Turing Award—and today, the ACM most excellently announced its agreement with the obvious. I have little to add to the prize citation (see also Lance’s post): from launching new fields whose reach extends beyond theory (PAC-learning), to proving epochal results (#P-completeness of the permanent), to asking hugely influential questions (permanent vs. determinant), Valiant has been a creative powerhouse of theoretical computer science for longer than I’ve been alive.

One thing the prize citation doesn’t mention is that Valiant is now the third Turing Award winner (after Andy Yao and Len Adleman) to have made a major contribution to quantum computing theory. Valiant’s 2001 paper Quantum Computers that can be Simulated Classically in Polynomial Time introduced the beautiful computational model that computer scientists now know as “matchgates,”and that physicists know as “noninteracting fermions.” It still amazes that Valiant proposed this model for purely mathematical reasons—hitting physical relevance straight between the eyes despite (as far as I can tell) not having that target anywhere in his sights.

To put the point in terms that my physicist friends will understand, that Valiant himself would probably dispute, but that I would defend:

Valiant’s work has shown that, even if our universe hadn’t been made of bosons and fermions, theoretical computer scientists would have had compelling reasons of their own to invent those particles or something equivalent to them—and furthermore, that at least one theoretical computer scientist would have had the imagination to do so.

On Wednesday, Larry Hardesty of the MIT News Office published a nice article about my work with Alex Arkhipov on the computational complexity of linear optics. Although the title—“The quantum singularity”—made me wince a little, I was impressed by the effort Larry put into getting the facts right, and especially laying out the problems that still need to be solved.

Less successful was a story in PC Magazine based on MIT’s press release, which contained the following sentence (let me know if you can decipher what the author meant—I couldn’t):

Aaronson says that he and Arkhipov have not successfully proven that designing a device capable of testing the theory is impossible—which is an important first step, whether to eventually building a quantum computer, or even just laying the initial framework for using the microscopic secrets of the universe to let humans better understand the world that surrounds them.

However, in the competition for Popular Science Article Sentence of the Year, the sentence above will have to contend with a now-classic sentence from the New York Times article about Watson:

More than anything, the contest was a vindication for the academic field of computer science, which began with great promise in the 1960s with the vision of creating a thinking machine and which became the laughingstock of Silicon Valley in the 1980s, when a series of heavily financed start-up companies went bankrupt.

To the NYT’s credit, they quickly posted a correction:

An article last Thursday about the I.B.M. computer Watson misidentified the academic field vindicated by Watson’s besting of two human opponents on “Jeopardy!” It is artificial intelligence — not computer science, a broader field that includes artificial intelligence.